Sequences And Series In Banach Spaces

Author : J. Diestel
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461252009

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Sequences and Series in Banach Spaces by J. Diestel Pdf

This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.

Author : Joseph Diestel
Publisher : Unknown
Page : 261 pages
File Size : 41,5 Mb
Release : 1984-01
Category : Banach spaces
ISBN : 3540908595

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Sequences and Series in Banach Spaces by Joseph Diestel Pdf

Author : Vladimir Kadets
Publisher : Birkhäuser
Page : 162 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891967

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Series in Banach Spaces by Vladimir Kadets Pdf

Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements.

Author : Sylvia Guerre-Delabriere
Publisher : CRC Press
Page : 234 pages
File Size : 42,6 Mb
Release : 1992-07-21
Category : Mathematics
ISBN : 0824787234

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Classical Sequences in Banach SPates by Sylvia Guerre-Delabriere Pdf

Author : William B. Johnson,Joram Lindenstrauss
Publisher : Elsevier
Page : 880 pages
File Size : 50,5 Mb
Release : 2001
Category : Banach spaces
ISBN : 0444513051

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Handbook of the Geometry of Banach Spaces by William B. Johnson,Joram Lindenstrauss Pdf

The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Author : P. K. Kamthan,Manjul Gupta
Publisher : Unknown
Page : 388 pages
File Size : 47,8 Mb
Release : 1981
Category : Computers
ISBN : STANFORD:36105032626835

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Sequence Spaces and Series by P. K. Kamthan,Manjul Gupta Pdf

Topological vector spaces; Sequences spaces; Conservence of series; Further developments in sequences spaces.

Author : Pawan K. Jain,Eberhard Malkowsky
Publisher : Alpha Science Int'l Ltd.
Page : 162 pages
File Size : 53,7 Mb
Release : 1999
Category : Mathematics
ISBN : 8173192391

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Sequence Spaces and Applications by Pawan K. Jain,Eberhard Malkowsky Pdf

This volume contains referred articles covering areas in classical as well as modern sequence space theory. The major topics covered are: classical sequence spaces; duals and matrix transformation; structure and topology; and applications. The book should be useful to postgraduates and the researchers working or intending to work in the areas of classical and the modern sequence space theory.

Author : J. Lindenstrauss,L. Tzafriri
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 53,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783642665578

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Classical Banach Spaces I by J. Lindenstrauss,L. Tzafriri Pdf

The appearance of Banach's book [8] in 1932 signified the beginning of a syste matic study of normed linear spaces, which have been the subject of continuous research ever since. In the sixties, and especially in the last decade, the research activity in this area grew considerably. As a result, Ban:ach space theory gained very much in depth as well as in scope: Most of its well known classical problems were solved, many interesting new directions were developed, and deep connections between Banach space theory and other areas of mathematics were established. The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces, with an emphasis on the study of the structure of the classical Banach spaces, that is C(K) and Lip.) and related spaces. We did not attempt to write a comprehensive survey of Banach space theory, or even only of the theory of classical Banach spaces, since the amount of interesting results on the subject makes such a survey practically impossible.

Author : Mohammad Mursaleen,Feyzi Başar
Publisher : CRC Press
Page : 313 pages
File Size : 45,6 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9781000045154

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Sequence Spaces by Mohammad Mursaleen,Feyzi Başar Pdf

This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.

Author : Pandelis Dodos
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 44,9 Mb
Release : 2010-05-10
Category : Mathematics
ISBN : 9783642121524

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Banach Spaces and Descriptive Set Theory: Selected Topics by Pandelis Dodos Pdf

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.

Author : Gokulananda Das,Sudarsan Nanda
Publisher : CRC Press
Page : 182 pages
File Size : 54,5 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 9781000467628

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Banach Limit and Applications by Gokulananda Das,Sudarsan Nanda Pdf

Banach Limits and Applications provides all the results in the area of Banach limit, its extensions, generalizations and applications to various fields in one go (as far as possible). All the results in this field, after Banach introduced this concept in the year 1932 , are scattered till now. Sublinear functionals generating and dominating Banach Limit, unique Branch Limit (almost convergence), invariant means and invariant limits, absolute and strong almost convergence, applications to ergodicity, law of large number, Fourier series, uniform distribution of sequences, uniform density, core theorems, functional Banach limits are discussed in this book. Discovery of functional analysis such as Hahn-Banach theorem, Banach-Steinhaus Theorem helped the researchers to develop a modern, rich and unified theory of sequence spaces by enveloping classical summability theory via matrix transformation and the topics related to sequence spaces arose from the concept of Banach limit are presented in this book. The unique features of this book are as follows: It contains all the results in this area at one place which are scattered till now. The book is first of its kinds in the sense that there is no other competitive book . The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area, the Ph.D. and advanced Masters students. The book is suitable for one or two semester course work for Ph. D. students, M.S. Students of North America and Europe, M. Phil and Masters Students of India.

Author : Pilar Cembranos,Jose Mendoza
Publisher : Springer
Page : 124 pages
File Size : 42,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696391

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Banach Spaces of Vector-Valued Functions by Pilar Cembranos,Jose Mendoza Pdf

"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.

Author : Joram Lindenstrauss,Lior Tzafriri
Publisher : Springer
Page : 254 pages
File Size : 40,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540377320

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Classical Banach Spaces by Joram Lindenstrauss,Lior Tzafriri Pdf

Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added. Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers.

Author : S. Nanda
Publisher : Alpha Science Int'l Ltd.
Page : 234 pages
File Size : 53,8 Mb
Release : 2005
Category : Mathematics
ISBN : 8173196028

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Sequences, Summability and Fourier Analysis by S. Nanda Pdf

Sequences, Summability and Fourier Analysis deals with various aspects of summability, a major branch of analysis. The subject grew extensively during the twentieth century through the contribution of eminent analysts, but there are numerous unsolved problems, which still baffle the present-day scholars, as the application side has been poorly attended to. This volume contains original research articles, many valuable survey articles on approximation theory, multivalent functions, almost convergence and absolute almost convergence, Tauberian theorems, Köthe-Toeplitz duals of sequence spaces, random Fourier series, stochastic integrals, interpolative subspaces of Banach space, metric transformations in sequence spaces, absolute summability and Nörlund summability.

Author : Fernando Albiac,Nigel J. Kalton
Publisher : Springer
Page : 508 pages
File Size : 46,5 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9783319315577

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Topics in Banach Space Theory by Fernando Albiac,Nigel J. Kalton Pdf

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews